Non-asymptotic fractional order differentiators via an algebraic parametric method

Da-Yan Liu; Olivier Gibaru; Wilfrid Perruquetti

hal-00713338, version 1

Non-asymptotic fractional order differentiators via an algebraic parametric method

Da-Yan Liu () ¹, Olivier Gibaru ^2, 3, Wilfrid Perruquetti ()^a^, 2, 4

1st International Conference on Systems and Computer Science (2012)

Résumé : Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations.

a – Ecole Centrale de Lille
1 : Estimation Modelling and ANalysis Group (KAUST-MCSE)
King Abdullah University of Science and Technology
2 : Non-A (INRIA Lille - Nord Europe)
INRIA : LILLE - NORD EUROPE
3 : Laboratoire des Sciences de l'Information et des Systèmes (LSIS)
CNRS : UMR6168 – Arts et Métiers ParisTech – Université Paul Cézanne - Aix-Marseille III – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I – Université Sud Toulon Var
4 : Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS)
CNRS : UMR8219 – Université Lille I - Sciences et technologies – Ecole Centrale de Lille

hal-00713338, version 1
http://hal.inria.fr/hal-00713338
oai:hal.inria.fr:hal-00713338
Contributeur : Da-Yan Liu <>
Soumis le : Samedi 30 Juin 2012, 13:33:04
Dernière modification le : Mercredi 19 Septembre 2012, 14:44:34

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PDF : $Icone de fractional_derivative.pdf$

PS : $Icone de fractional_derivative.ps$

arXiv : 1207.0129

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